
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include <cerrno>
#include <cstdlib>
#include <ctime>
#include <fstream>
#include <functional>
#include <iostream>
#include <sstream>
#include <string>
#include <typeinfo>
#include <vector>

// The following includes of STL headers have to be done _before_ the
// definition of macros min() and max().  The reason is that many STL
// implementations will not work properly as the min and max symbols collide
// with the STL functions std:min() and std::max().  The STL headers may check
// for the macro definition of min/max and issue a warning or undefine the
// macros.
//
// Still, Windows defines min() and max() in windef.h as part of the regular
// Windows system interfaces and many other Windows APIs depend on these
// macros being available.  To prevent the macro expansion of min/max and to
// make Eigen compatible with the Windows environment all function calls of
// std::min() and std::max() have to be written with parenthesis around the
// function name.
//
// All STL headers used by Eigen should be included here.  Because main.h is
// included before any Eigen header and because the STL headers are guarded
// against multiple inclusions, no STL header will see our own min/max macro
// definitions.
#include <algorithm>
#include <limits>
// Disable ICC's std::complex operator specializations so we can use our own.
#define _OVERRIDE_COMPLEX_SPECIALIZATION_ 1
#include <cassert>
#include <complex>
#include <deque>
#include <list>
#include <queue>
#if __cplusplus >= 201103L || (defined(_MSVC_LANG) && _MSVC_LANG >= 201103L)
#include <chrono>
#include <random>
#ifdef EIGEN_USE_THREADS
#include <future>
#endif
#endif

// Same for cuda_fp16.h
#if defined(__CUDACC__) && !defined(EIGEN_NO_CUDA)
// Means the compiler is either nvcc or clang with CUDA enabled
#define EIGEN_CUDACC __CUDACC__
#endif
#if defined(EIGEN_CUDACC)
#include <cuda.h>
#define EIGEN_CUDA_SDK_VER (CUDA_VERSION * 10)
#else
#define EIGEN_CUDA_SDK_VER 0
#endif
#if EIGEN_CUDA_SDK_VER >= 70500
#include <cuda_fp16.h>
#endif

// To test that all calls from Eigen code to std::min() and std::max() are
// protected by parenthesis against macro expansion, the min()/max() macros
// are defined here and any not-parenthesized min/max call will cause a
// compiler error.
#if !defined(__HIPCC__) && !defined(EIGEN_USE_SYCL)
//
// HIP header files include the following files
//  <thread>
//  <regex>
//  <unordered_map>
// which seem to contain not-parenthesized calls to "max"/"min", triggering the following check and causing the compile
// to fail
//
// Including those header files before the following macro definition for "min" / "max", only partially resolves the
// issue This is because other HIP header files also define "isnan" / "isinf" / "isfinite" functions, which are needed
// in other headers.
//
// So instead choosing to simply disable this check for HIP
//
#define min(A, B) please_protect_your_min_with_parentheses
#define max(A, B) please_protect_your_max_with_parentheses
#define isnan(X) please_protect_your_isnan_with_parentheses
#define isinf(X) please_protect_your_isinf_with_parentheses
#define isfinite(X) please_protect_your_isfinite_with_parentheses
#endif

// test possible conflicts
struct real
{};
struct imag
{};

#ifdef M_PI
#undef M_PI
#endif
#define M_PI please_use_EIGEN_PI_instead_of_M_PI

#define FORBIDDEN_IDENTIFIER                                                                                           \
	(this_identifier_is_forbidden_to_avoid_clashes) this_identifier_is_forbidden_to_avoid_clashes
// B0 is defined in POSIX header termios.h
#define B0 FORBIDDEN_IDENTIFIER
// `I` may be defined by complex.h:
#define I FORBIDDEN_IDENTIFIER

// Unit tests calling Eigen's blas library must preserve the default blocking size
// to avoid troubles.
#ifndef EIGEN_NO_DEBUG_SMALL_PRODUCT_BLOCKS
#define EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS
#endif

// shuts down ICC's remark #593: variable "XXX" was set but never used
#define TEST_SET_BUT_UNUSED_VARIABLE(X) EIGEN_UNUSED_VARIABLE(X)

#ifdef TEST_ENABLE_TEMPORARY_TRACKING

static long int nb_temporaries;
static long int nb_temporaries_on_assert = -1;

inline void
on_temporary_creation(long int size)
{
	// here's a great place to set a breakpoint when debugging failures in this test!
	if (size != 0)
		nb_temporaries++;
	if (nb_temporaries_on_assert > 0)
		assert(nb_temporaries < nb_temporaries_on_assert);
}

#define EIGEN_DENSE_STORAGE_CTOR_PLUGIN                                                                                \
	{                                                                                                                  \
		on_temporary_creation(size);                                                                                   \
	}

#define VERIFY_EVALUATION_COUNT(XPR, N)                                                                                \
	{                                                                                                                  \
		nb_temporaries = 0;                                                                                            \
		XPR;                                                                                                           \
		if (nb_temporaries != (N)) {                                                                                   \
			std::cerr << "nb_temporaries == " << nb_temporaries << "\n";                                               \
		}                                                                                                              \
		VERIFY((#XPR) && nb_temporaries == (N));                                                                       \
	}

#endif

#include "split_test_helper.h"

#ifdef NDEBUG
#undef NDEBUG
#endif

// On windows CE, NDEBUG is automatically defined <assert.h> if NDEBUG is not defined.
#ifndef DEBUG
#define DEBUG
#endif

// bounds integer values for AltiVec
#if defined(__ALTIVEC__) || defined(__VSX__)
#define EIGEN_MAKING_DOCS
#endif

#define DEFAULT_REPEAT 10

namespace Eigen {
static std::vector<std::string> g_test_stack;
// level == 0 <=> abort if test fail
// level >= 1 <=> warning message to std::cerr if test fail
static int g_test_level = 0;
static int g_repeat = 1;
static unsigned int g_seed = 0;
static bool g_has_set_repeat = false, g_has_set_seed = false;

class EigenTest
{
  public:
	EigenTest()
		: m_func(0)
	{
	}
	EigenTest(const char* a_name, void (*func)(void))
		: m_name(a_name)
		, m_func(func)
	{
		get_registered_tests().push_back(this);
	}
	const std::string& name() const { return m_name; }
	void operator()() const { m_func(); }

	static const std::vector<EigenTest*>& all() { return get_registered_tests(); }

  protected:
	static std::vector<EigenTest*>& get_registered_tests()
	{
		static std::vector<EigenTest*>* ms_registered_tests = new std::vector<EigenTest*>();
		return *ms_registered_tests;
	}
	std::string m_name;
	void (*m_func)(void);
};

// Declare and register a test, e.g.:
//    EIGEN_DECLARE_TEST(mytest) { ... }
// will create a function:
//    void test_mytest() { ... }
// that will be automatically called.
#define EIGEN_DECLARE_TEST(X)                                                                                          \
	void EIGEN_CAT(test_, X)();                                                                                        \
	static EigenTest EIGEN_CAT(test_handler_, X)(EIGEN_MAKESTRING(X), &EIGEN_CAT(test_, X));                           \
	void EIGEN_CAT(test_, X)()
}

#define TRACK std::cerr << __FILE__ << " " << __LINE__ << std::endl
// #define TRACK while()

#define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, "  ", "\n", "", "", "", "")

#if (defined(_CPPUNWIND) || defined(__EXCEPTIONS)) && !defined(__CUDA_ARCH__) && !defined(__HIP_DEVICE_COMPILE__) &&   \
	!defined(__SYCL_DEVICE_ONLY__)
#define EIGEN_EXCEPTIONS
#endif

#ifndef EIGEN_NO_ASSERTION_CHECKING

namespace Eigen {
static const bool should_raise_an_assert = false;

// Used to avoid to raise two exceptions at a time in which
// case the exception is not properly caught.
// This may happen when a second exceptions is triggered in a destructor.
static bool no_more_assert = false;
static bool report_on_cerr_on_assert_failure = true;

struct eigen_assert_exception
{
	eigen_assert_exception(void) {}
	~eigen_assert_exception() { Eigen::no_more_assert = false; }
};

struct eigen_static_assert_exception
{
	eigen_static_assert_exception(void) {}
	~eigen_static_assert_exception() { Eigen::no_more_assert = false; }
};
}
// If EIGEN_DEBUG_ASSERTS is defined and if no assertion is triggered while
// one should have been, then the list of executed assertions is printed out.
//
// EIGEN_DEBUG_ASSERTS is not enabled by default as it
// significantly increases the compilation time
// and might even introduce side effects that would hide
// some memory errors.
#ifdef EIGEN_DEBUG_ASSERTS

namespace Eigen {
namespace internal {
static bool push_assert = false;
}
static std::vector<std::string> eigen_assert_list;
}
#define eigen_assert(a)                                                                                                \
	if ((!(a)) && (!no_more_assert)) {                                                                                 \
		if (report_on_cerr_on_assert_failure)                                                                          \
			std::cerr << #a << " " __FILE__ << "(" << __LINE__ << ")\n";                                               \
		Eigen::no_more_assert = true;                                                                                  \
		EIGEN_THROW_X(Eigen::eigen_assert_exception());                                                                \
	} else if (Eigen::internal::push_assert) {                                                                         \
		eigen_assert_list.push_back(                                                                                   \
			std::string(EIGEN_MAKESTRING(__FILE__) " (" EIGEN_MAKESTRING(__LINE__) ") : " #a));                        \
	}

#ifdef EIGEN_EXCEPTIONS
#define VERIFY_RAISES_ASSERT(a)                                                                                        \
	{                                                                                                                  \
		Eigen::no_more_assert = false;                                                                                 \
		Eigen::eigen_assert_list.clear();                                                                              \
		Eigen::internal::push_assert = true;                                                                           \
		Eigen::report_on_cerr_on_assert_failure = false;                                                               \
		try {                                                                                                          \
			a;                                                                                                         \
			std::cerr << "One of the following asserts should have been triggered:\n";                                 \
			for (uint ai = 0; ai < eigen_assert_list.size(); ++ai)                                                     \
				std::cerr << "  " << eigen_assert_list[ai] << "\n";                                                    \
			VERIFY(Eigen::should_raise_an_assert&& #a);                                                                \
		} catch (Eigen::eigen_assert_exception) {                                                                      \
			Eigen::internal::push_assert = false;                                                                      \
			VERIFY(true);                                                                                              \
		}                                                                                                              \
		Eigen::report_on_cerr_on_assert_failure = true;                                                                \
		Eigen::internal::push_assert = false;                                                                          \
	}
#endif // EIGEN_EXCEPTIONS

#elif !defined(__CUDACC__) && !defined(__HIPCC__) && !defined(SYCL_DEVICE_ONLY) // EIGEN_DEBUG_ASSERTS
// see bug 89. The copy_bool here is working around a bug in gcc <= 4.3
#define eigen_assert(a)                                                                                                \
	if ((!Eigen::internal::copy_bool(a)) && (!no_more_assert)) {                                                       \
		Eigen::no_more_assert = true;                                                                                  \
		if (report_on_cerr_on_assert_failure)                                                                          \
			eigen_plain_assert(a);                                                                                     \
		else                                                                                                           \
			EIGEN_THROW_X(Eigen::eigen_assert_exception());                                                            \
	}

#ifdef EIGEN_EXCEPTIONS
#define VERIFY_RAISES_ASSERT(a)                                                                                        \
	{                                                                                                                  \
		Eigen::no_more_assert = false;                                                                                 \
		Eigen::report_on_cerr_on_assert_failure = false;                                                               \
		try {                                                                                                          \
			a;                                                                                                         \
			VERIFY(Eigen::should_raise_an_assert&& #a);                                                                \
		} catch (Eigen::eigen_assert_exception&) {                                                                     \
			VERIFY(true);                                                                                              \
		}                                                                                                              \
		Eigen::report_on_cerr_on_assert_failure = true;                                                                \
	}
#endif // EIGEN_EXCEPTIONS
#endif // EIGEN_DEBUG_ASSERTS

#if defined(TEST_CHECK_STATIC_ASSERTIONS) && defined(EIGEN_EXCEPTIONS)
#define EIGEN_STATIC_ASSERT(a, MSG)                                                                                    \
	if ((!Eigen::internal::copy_bool(a)) && (!no_more_assert)) {                                                       \
		Eigen::no_more_assert = true;                                                                                  \
		if (report_on_cerr_on_assert_failure)                                                                          \
			eigen_plain_assert((a) && #MSG);                                                                           \
		else                                                                                                           \
			EIGEN_THROW_X(Eigen::eigen_static_assert_exception());                                                     \
	}
#define VERIFY_RAISES_STATIC_ASSERT(a)                                                                                 \
	{                                                                                                                  \
		Eigen::no_more_assert = false;                                                                                 \
		Eigen::report_on_cerr_on_assert_failure = false;                                                               \
		try {                                                                                                          \
			a;                                                                                                         \
			VERIFY(Eigen::should_raise_an_assert&& #a);                                                                \
		} catch (Eigen::eigen_static_assert_exception&) {                                                              \
			VERIFY(true);                                                                                              \
		}                                                                                                              \
		Eigen::report_on_cerr_on_assert_failure = true;                                                                \
	}
#endif // TEST_CHECK_STATIC_ASSERTIONS

#ifndef VERIFY_RAISES_ASSERT
#define VERIFY_RAISES_ASSERT(a) std::cout << "Can't VERIFY_RAISES_ASSERT( " #a " ) with exceptions disabled\n";
#endif
#ifndef VERIFY_RAISES_STATIC_ASSERT
#define VERIFY_RAISES_STATIC_ASSERT(a)                                                                                 \
	std::cout << "Can't VERIFY_RAISES_STATIC_ASSERT( " #a " ) with exceptions disabled\n";
#endif

#if !defined(__CUDACC__) && !defined(__HIPCC__) && !defined(SYCL_DEVICE_ONLY)
#define EIGEN_USE_CUSTOM_ASSERT
#endif

#else // EIGEN_NO_ASSERTION_CHECKING

#define VERIFY_RAISES_ASSERT(a)                                                                                        \
	{                                                                                                                  \
	}
#define VERIFY_RAISES_STATIC_ASSERT(a)                                                                                 \
	{                                                                                                                  \
	}

#endif // EIGEN_NO_ASSERTION_CHECKING

#define EIGEN_INTERNAL_DEBUGGING
#include <Eigen/QR> // required for createRandomPIMatrixOfRank

inline void
verify_impl(bool condition, const char* testname, const char* file, int line, const char* condition_as_string)
{
	if (!condition) {
		if (Eigen::g_test_level > 0)
			std::cerr << "WARNING: ";
		std::cerr << "Test " << testname << " failed in " << file << " (" << line << ")" << std::endl
				  << "    " << condition_as_string << std::endl;
		std::cerr << "Stack:\n";
		const int test_stack_size = static_cast<int>(Eigen::g_test_stack.size());
		for (int i = test_stack_size - 1; i >= 0; --i)
			std::cerr << "  - " << Eigen::g_test_stack[i] << "\n";
		std::cerr << "\n";
		if (Eigen::g_test_level == 0)
			abort();
	}
}

#define VERIFY(a) ::verify_impl(a, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a))

#define VERIFY_GE(a, b) ::verify_impl(a >= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a >= b))
#define VERIFY_LE(a, b) ::verify_impl(a <= b, g_test_stack.back().c_str(), __FILE__, __LINE__, EIGEN_MAKESTRING(a <= b))

#define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b, true))
#define VERIFY_IS_NOT_EQUAL(a, b) VERIFY(test_is_equal(a, b, false))
#define VERIFY_IS_APPROX(a, b) VERIFY(verifyIsApprox(a, b))
#define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b))
#define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b))
#define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b))
#define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b))
#define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b))

#define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a))

#define STATIC_CHECK(COND) EIGEN_STATIC_ASSERT((COND), EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT)

#define CALL_SUBTEST(FUNC)                                                                                             \
	do {                                                                                                               \
		g_test_stack.push_back(EIGEN_MAKESTRING(FUNC));                                                                \
		FUNC;                                                                                                          \
		g_test_stack.pop_back();                                                                                       \
	} while (0)

namespace Eigen {

template<typename T1, typename T2>
typename internal::enable_if<internal::is_same<T1, T2>::value, bool>::type
is_same_type(const T1&, const T2&)
{
	return true;
}

template<typename T>
inline typename NumTraits<T>::Real
test_precision()
{
	return NumTraits<T>::dummy_precision();
}
template<>
inline float
test_precision<float>()
{
	return 1e-3f;
}
template<>
inline double
test_precision<double>()
{
	return 1e-6;
}
template<>
inline long double
test_precision<long double>()
{
	return 1e-6l;
}
template<>
inline float
test_precision<std::complex<float>>()
{
	return test_precision<float>();
}
template<>
inline double
test_precision<std::complex<double>>()
{
	return test_precision<double>();
}
template<>
inline long double
test_precision<std::complex<long double>>()
{
	return test_precision<long double>();
}

#define EIGEN_TEST_SCALAR_TEST_OVERLOAD(TYPE)                                                                          \
	inline bool test_isApprox(TYPE a, TYPE b)                                                                          \
	{                                                                                                                  \
		return internal::isApprox(a, b, test_precision<TYPE>());                                                       \
	}                                                                                                                  \
	inline bool test_isMuchSmallerThan(TYPE a, TYPE b)                                                                 \
	{                                                                                                                  \
		return internal::isMuchSmallerThan(a, b, test_precision<TYPE>());                                              \
	}                                                                                                                  \
	inline bool test_isApproxOrLessThan(TYPE a, TYPE b)                                                                \
	{                                                                                                                  \
		return internal::isApproxOrLessThan(a, b, test_precision<TYPE>());                                             \
	}

EIGEN_TEST_SCALAR_TEST_OVERLOAD(short)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned short)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(int)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned int)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(long)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long)
#if EIGEN_HAS_CXX11
EIGEN_TEST_SCALAR_TEST_OVERLOAD(long long)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(unsigned long long)
#endif
EIGEN_TEST_SCALAR_TEST_OVERLOAD(float)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(double)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(half)
EIGEN_TEST_SCALAR_TEST_OVERLOAD(bfloat16)

#undef EIGEN_TEST_SCALAR_TEST_OVERLOAD

#ifndef EIGEN_TEST_NO_COMPLEX
inline bool
test_isApprox(const std::complex<float>& a, const std::complex<float>& b)
{
	return internal::isApprox(a, b, test_precision<std::complex<float>>());
}
inline bool
test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
{
	return internal::isMuchSmallerThan(a, b, test_precision<std::complex<float>>());
}

inline bool
test_isApprox(const std::complex<double>& a, const std::complex<double>& b)
{
	return internal::isApprox(a, b, test_precision<std::complex<double>>());
}
inline bool
test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
{
	return internal::isMuchSmallerThan(a, b, test_precision<std::complex<double>>());
}

#ifndef EIGEN_TEST_NO_LONGDOUBLE
inline bool
test_isApprox(const std::complex<long double>& a, const std::complex<long double>& b)
{
	return internal::isApprox(a, b, test_precision<std::complex<long double>>());
}
inline bool
test_isMuchSmallerThan(const std::complex<long double>& a, const std::complex<long double>& b)
{
	return internal::isMuchSmallerThan(a, b, test_precision<std::complex<long double>>());
}
#endif
#endif

#ifndef EIGEN_TEST_NO_LONGDOUBLE
inline bool
test_isApprox(const long double& a, const long double& b)
{
	bool ret = internal::isApprox(a, b, test_precision<long double>());
	if (!ret)
		std::cerr << std::endl
				  << "    actual   = " << a << std::endl
				  << "    expected = " << b << std::endl
				  << std::endl;
	return ret;
}

inline bool
test_isMuchSmallerThan(const long double& a, const long double& b)
{
	return internal::isMuchSmallerThan(a, b, test_precision<long double>());
}
inline bool
test_isApproxOrLessThan(const long double& a, const long double& b)
{
	return internal::isApproxOrLessThan(a, b, test_precision<long double>());
}
#endif // EIGEN_TEST_NO_LONGDOUBLE

// test_relative_error returns the relative difference between a and b as a real scalar as used in isApprox.
template<typename T1, typename T2>
typename NumTraits<typename T1::RealScalar>::NonInteger
test_relative_error(const EigenBase<T1>& a, const EigenBase<T2>& b)
{
	using std::sqrt;
	typedef typename NumTraits<typename T1::RealScalar>::NonInteger RealScalar;
	typename internal::nested_eval<T1, 2>::type ea(a.derived());
	typename internal::nested_eval<T2, 2>::type eb(b.derived());
	return sqrt(RealScalar((ea - eb).cwiseAbs2().sum()) /
				RealScalar((std::min)(eb.cwiseAbs2().sum(), ea.cwiseAbs2().sum())));
}

template<typename T1, typename T2>
typename T1::RealScalar
test_relative_error(const T1& a, const T2& b, const typename T1::Coefficients* = 0)
{
	return test_relative_error(a.coeffs(), b.coeffs());
}

template<typename T1, typename T2>
typename T1::Scalar
test_relative_error(const T1& a, const T2& b, const typename T1::MatrixType* = 0)
{
	return test_relative_error(a.matrix(), b.matrix());
}

template<typename S, int D>
S
test_relative_error(const Translation<S, D>& a, const Translation<S, D>& b)
{
	return test_relative_error(a.vector(), b.vector());
}

template<typename S, int D, int O>
S
test_relative_error(const ParametrizedLine<S, D, O>& a, const ParametrizedLine<S, D, O>& b)
{
	return (std::max)(test_relative_error(a.origin(), b.origin()), test_relative_error(a.origin(), b.origin()));
}

template<typename S, int D>
S
test_relative_error(const AlignedBox<S, D>& a, const AlignedBox<S, D>& b)
{
	return (std::max)(test_relative_error((a.min)(), (b.min)()), test_relative_error((a.max)(), (b.max)()));
}

template<typename Derived>
class SparseMatrixBase;
template<typename T1, typename T2>
typename T1::RealScalar
test_relative_error(const MatrixBase<T1>& a, const SparseMatrixBase<T2>& b)
{
	return test_relative_error(a, b.toDense());
}

template<typename Derived>
class SparseMatrixBase;
template<typename T1, typename T2>
typename T1::RealScalar
test_relative_error(const SparseMatrixBase<T1>& a, const MatrixBase<T2>& b)
{
	return test_relative_error(a.toDense(), b);
}

template<typename Derived>
class SparseMatrixBase;
template<typename T1, typename T2>
typename T1::RealScalar
test_relative_error(const SparseMatrixBase<T1>& a, const SparseMatrixBase<T2>& b)
{
	return test_relative_error(a.toDense(), b.toDense());
}

template<typename T1, typename T2>
typename NumTraits<typename NumTraits<T1>::Real>::NonInteger
test_relative_error(
	const T1& a,
	const T2& b,
	typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T1>::Real>::value, T1>::type* = 0)
{
	typedef typename NumTraits<typename NumTraits<T1>::Real>::NonInteger RealScalar;
	return numext::sqrt(RealScalar(numext::abs2(a - b)) /
						(numext::mini)(RealScalar(numext::abs2(a)), RealScalar(numext::abs2(b))));
}

template<typename T>
T
test_relative_error(const Rotation2D<T>& a, const Rotation2D<T>& b)
{
	return test_relative_error(a.angle(), b.angle());
}

template<typename T>
T
test_relative_error(const AngleAxis<T>& a, const AngleAxis<T>& b)
{
	return (std::max)(test_relative_error(a.angle(), b.angle()), test_relative_error(a.axis(), b.axis()));
}

template<typename Type1, typename Type2>
inline bool
test_isApprox(const Type1& a, const Type2& b, typename Type1::Scalar* = 0) // Enabled for Eigen's type only
{
	return a.isApprox(b, test_precision<typename Type1::Scalar>());
}

// get_test_precision is a small wrapper to test_precision allowing to return the scalar precision for either scalars or
// expressions
template<typename T>
typename NumTraits<typename T::Scalar>::Real
get_test_precision(const T&, const typename T::Scalar* = 0)
{
	return test_precision<typename NumTraits<typename T::Scalar>::Real>();
}

template<typename T>
typename NumTraits<T>::Real
get_test_precision(
	const T&,
	typename internal::enable_if<internal::is_arithmetic<typename NumTraits<T>::Real>::value, T>::type* = 0)
{
	return test_precision<typename NumTraits<T>::Real>();
}

// verifyIsApprox is a wrapper to test_isApprox that outputs the relative difference magnitude if the test fails.
template<typename Type1, typename Type2>
inline bool
verifyIsApprox(const Type1& a, const Type2& b)
{
	bool ret = test_isApprox(a, b);
	if (!ret) {
		std::cerr << "Difference too large wrt tolerance " << get_test_precision(a)
				  << ", relative error is: " << test_relative_error(a, b) << std::endl;
	}
	return ret;
}

// The idea behind this function is to compare the two scalars a and b where
// the scalar ref is a hint about the expected order of magnitude of a and b.
// WARNING: the scalar a and b must be positive
// Therefore, if for some reason a and b are very small compared to ref,
// we won't issue a false negative.
// This test could be: abs(a-b) <= eps * ref
// However, it seems that simply comparing a+ref and b+ref is more sensitive to true error.
template<typename Scalar, typename ScalarRef>
inline bool
test_isApproxWithRef(const Scalar& a, const Scalar& b, const ScalarRef& ref)
{
	return test_isApprox(a + ref, b + ref);
}

template<typename Derived1, typename Derived2>
inline bool
test_isMuchSmallerThan(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2)
{
	return m1.isMuchSmallerThan(m2, test_precision<typename internal::traits<Derived1>::Scalar>());
}

template<typename Derived>
inline bool
test_isMuchSmallerThan(const MatrixBase<Derived>& m,
					   const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real& s)
{
	return m.isMuchSmallerThan(s, test_precision<typename internal::traits<Derived>::Scalar>());
}

template<typename Derived>
inline bool
test_isUnitary(const MatrixBase<Derived>& m)
{
	return m.isUnitary(test_precision<typename internal::traits<Derived>::Scalar>());
}

// Forward declaration to avoid ICC warning
template<typename T, typename U>
bool
test_is_equal(const T& actual, const U& expected, bool expect_equal = true);

template<typename T, typename U>
bool
test_is_equal(const T& actual, const U& expected, bool expect_equal)
{
	if ((actual == expected) == expect_equal)
		return true;
	// false:
	std::cerr << "\n    actual   = " << actual << "\n    expected " << (expect_equal ? "= " : "!=") << expected
			  << "\n\n";
	return false;
}

/** Creates a random Partial Isometry matrix of given rank.
 *
 * A partial isometry is a matrix all of whose singular values are either 0 or 1.
 * This is very useful to test rank-revealing algorithms.
 */
// Forward declaration to avoid ICC warning
template<typename MatrixType>
void
createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);
template<typename MatrixType>
void
createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m)
{
	typedef typename internal::traits<MatrixType>::Scalar Scalar;
	enum
	{
		Rows = MatrixType::RowsAtCompileTime,
		Cols = MatrixType::ColsAtCompileTime
	};

	typedef Matrix<Scalar, Dynamic, 1> VectorType;
	typedef Matrix<Scalar, Rows, Rows> MatrixAType;
	typedef Matrix<Scalar, Cols, Cols> MatrixBType;

	if (desired_rank == 0) {
		m.setZero(rows, cols);
		return;
	}

	if (desired_rank == 1) {
		// here we normalize the vectors to get a partial isometry
		m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();
		return;
	}

	MatrixAType a = MatrixAType::Random(rows, rows);
	MatrixType d = MatrixType::Identity(rows, cols);
	MatrixBType b = MatrixBType::Random(cols, cols);

	// set the diagonal such that only desired_rank non-zero entries reamain
	const Index diag_size = (std::min)(d.rows(), d.cols());
	if (diag_size != desired_rank)
		d.diagonal().segment(desired_rank, diag_size - desired_rank) = VectorType::Zero(diag_size - desired_rank);

	HouseholderQR<MatrixAType> qra(a);
	HouseholderQR<MatrixBType> qrb(b);
	m = qra.householderQ() * d * qrb.householderQ();
}

// Forward declaration to avoid ICC warning
template<typename PermutationVectorType>
void
randomPermutationVector(PermutationVectorType& v, Index size);
template<typename PermutationVectorType>
void
randomPermutationVector(PermutationVectorType& v, Index size)
{
	typedef typename PermutationVectorType::Scalar Scalar;
	v.resize(size);
	for (Index i = 0; i < size; ++i)
		v(i) = Scalar(i);
	if (size == 1)
		return;
	for (Index n = 0; n < 3 * size; ++n) {
		Index i = internal::random<Index>(0, size - 1);
		Index j;
		do
			j = internal::random<Index>(0, size - 1);
		while (j == i);
		std::swap(v(i), v(j));
	}
}

template<typename T>
bool
isNotNaN(const T& x)
{
	return x == x;
}

template<typename T>
bool
isPlusInf(const T& x)
{
	return x > NumTraits<T>::highest();
}

template<typename T>
bool
isMinusInf(const T& x)
{
	return x < NumTraits<T>::lowest();
}

} // end namespace Eigen

template<typename T>
struct GetDifferentType;

template<>
struct GetDifferentType<float>
{
	typedef double type;
};
template<>
struct GetDifferentType<double>
{
	typedef float type;
};
template<typename T>
struct GetDifferentType<std::complex<T>>
{
	typedef std::complex<typename GetDifferentType<T>::type> type;
};

// Forward declaration to avoid ICC warning
template<typename T>
std::string
type_name();
template<typename T>
std::string
type_name()
{
	return "other";
}
template<>
std::string
type_name<float>()
{
	return "float";
}
template<>
std::string
type_name<double>()
{
	return "double";
}
template<>
std::string
type_name<long double>()
{
	return "long double";
}
template<>
std::string
type_name<int>()
{
	return "int";
}
template<>
std::string
type_name<std::complex<float>>()
{
	return "complex<float>";
}
template<>
std::string
type_name<std::complex<double>>()
{
	return "complex<double>";
}
template<>
std::string
type_name<std::complex<long double>>()
{
	return "complex<long double>";
}
template<>
std::string
type_name<std::complex<int>>()
{
	return "complex<int>";
}

using namespace Eigen;

inline void
set_repeat_from_string(const char* str)
{
	errno = 0;
	g_repeat = int(strtoul(str, 0, 10));
	if (errno || g_repeat <= 0) {
		std::cout << "Invalid repeat value " << str << std::endl;
		exit(EXIT_FAILURE);
	}
	g_has_set_repeat = true;
}

inline void
set_seed_from_string(const char* str)
{
	errno = 0;
	g_seed = int(strtoul(str, 0, 10));
	if (errno || g_seed == 0) {
		std::cout << "Invalid seed value " << str << std::endl;
		exit(EXIT_FAILURE);
	}
	g_has_set_seed = true;
}

int
main(int argc, char* argv[])
{
	g_has_set_repeat = false;
	g_has_set_seed = false;
	bool need_help = false;

	for (int i = 1; i < argc; i++) {
		if (argv[i][0] == 'r') {
			if (g_has_set_repeat) {
				std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
				return 1;
			}
			set_repeat_from_string(argv[i] + 1);
		} else if (argv[i][0] == 's') {
			if (g_has_set_seed) {
				std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
				return 1;
			}
			set_seed_from_string(argv[i] + 1);
		} else {
			need_help = true;
		}
	}

	if (need_help) {
		std::cout << "This test application takes the following optional arguments:" << std::endl;
		std::cout << "  rN     Repeat each test N times (default: " << DEFAULT_REPEAT << ")" << std::endl;
		std::cout << "  sN     Use N as seed for random numbers (default: based on current time)" << std::endl;
		std::cout << std::endl;
		std::cout << "If defined, the environment variables EIGEN_REPEAT and EIGEN_SEED" << std::endl;
		std::cout << "will be used as default values for these parameters." << std::endl;
		return 1;
	}

	char* env_EIGEN_REPEAT = getenv("EIGEN_REPEAT");
	if (!g_has_set_repeat && env_EIGEN_REPEAT)
		set_repeat_from_string(env_EIGEN_REPEAT);
	char* env_EIGEN_SEED = getenv("EIGEN_SEED");
	if (!g_has_set_seed && env_EIGEN_SEED)
		set_seed_from_string(env_EIGEN_SEED);

	if (!g_has_set_seed)
		g_seed = (unsigned int)time(NULL);
	if (!g_has_set_repeat)
		g_repeat = DEFAULT_REPEAT;

	std::cout << "Initializing random number generator with seed " << g_seed << std::endl;
	std::stringstream ss;
	ss << "Seed: " << g_seed;
	g_test_stack.push_back(ss.str());
	srand(g_seed);
	std::cout << "Repeating each test " << g_repeat << " times" << std::endl;

	VERIFY(EigenTest::all().size() > 0);

	for (std::size_t i = 0; i < EigenTest::all().size(); ++i) {
		const EigenTest& current_test = *EigenTest::all()[i];
		Eigen::g_test_stack.push_back(current_test.name());
		current_test();
		Eigen::g_test_stack.pop_back();
	}

	return 0;
}

// These warning are disabled here such that they are still ON when parsing Eigen's header files.
#if defined __INTEL_COMPILER
// remark #383: value copied to temporary, reference to temporary used
//  -> this warning is raised even for legal usage as: g_test_stack.push_back("foo"); where g_test_stack is a
//  std::vector<std::string>
// remark #1418: external function definition with no prior declaration
//  -> this warning is raised for all our test functions. Declaring them static would fix the issue.
// warning #279: controlling expression is constant
// remark #1572: floating-point equality and inequality comparisons are unreliable
#pragma warning disable 279 383 1418 1572
#endif

#ifdef _MSC_VER
// 4503 - decorated name length exceeded, name was truncated
#pragma warning(disable : 4503)
#endif
